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Simplifying 3(12 + 2d) + -7 = 13 + -1(12 + 2d) (12 * 3 + 2d * 3) + -7 = 13 + -1(12 + 2d) (36 + 6d) + -7 = 13 + -1(12 + 2d) Reorder the terms: 36 + -7 + 6d = 13 + -1(12 + 2d) Combine like terms: 36 + -7 = 29 29 + 6d = 13 + -1(12 + 2d) 29 + 6d = 13 + (12 * -1 + 2d * -1) 29 + 6d = 13 + (-12 + -2d) Combine like terms: 13 + -12 = 1 29 + 6d = 1 + -2d Solving 29 + 6d = 1 + -2d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2d' to each side of the equation. 29 + 6d + 2d = 1 + -2d + 2d Combine like terms: 6d + 2d = 8d 29 + 8d = 1 + -2d + 2d Combine like terms: -2d + 2d = 0 29 + 8d = 1 + 0 29 + 8d = 1 Add '-29' to each side of the equation. 29 + -29 + 8d = 1 + -29 Combine like terms: 29 + -29 = 0 0 + 8d = 1 + -29 8d = 1 + -29 Combine like terms: 1 + -29 = -28 8d = -28 Divide each side by '8'. d = -3.5 Simplifying d = -3.5
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